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From Luc Maisonobe <Luc.Maison...@free.fr>
Subject Re: [math] Rotation around given direction
Date Mon, 08 Jul 2013 15:13:36 GMT
Hi Alexander,

Le 08/07/2013 14:44, Alexander Nozik a écrit :
>  In order to solve some Monte-Carlo problem I need to implement the
> following procedure: during interaction I know the difference between
> the initial and the final angle "dTheta" (the direction is random) and
> the initial polar angle "theta" (using notation like here
> http://en.wikipedia.org/wiki/Spherical_coordinate_system#Cartesian_coordinates).
> What i need to know is the final polar angle. Azimuthal angle does not
> matter.
> In order to do so I am creating two vectors with polar angles "theta"
> and "theta + dTheta" and trying to rotate one around the other for a
> random angle "phi" (phi could be fixed as well, it does not matter).
> What i don't understand is why the angle between the final vector and
> the initial one is not "dTheta"?
> 
> I use the following code:
> 
>    double addTheta(double theta, double dTheta) {
>         double phi = generator.next() * 2 * Math.PI;
>         SphericalCoordinates init = new SphericalCoordinates(1, 0,
> theta+dTheta);
>         SphericalCoordinates rotate = new SphericalCoordinates(1, 0,
> theta);
>         Rotation rot = new Rotation(rotate.getCartesian(), phi);
> 
>         Vector3D result = rot.applyTo(init.getCartesian());
> 
>         assert Vector3D.angle(result, init.getCartesian()) == dTheta;

The angle that should be equalt to dTheta is the angle between result
and rotate.getCartesian(), not the angle between result and
init.getCartesian(). The latter can take any value between 0 and 2 * dTheta.

best regards,
Luc

>         return Math.acos(result.getZ());
> 
>     }
> 
> Thanks in advance.
> 
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